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Based on the Fokker-Planck equation along with laser propagation equation, a theoretical model that describes the ultrashort-pulse laser propagation characteristics and breakdown in dielectrics is established. Using this model, the conduction band electron densities and the electric field intensities at different positions in a dielectric material at different time are calculated. The variations of reflection, transmittance and energy deposition rate with input laser energy density are discussed. With the threshold conduction band electron density criterion, the breakdown depth in the material under varying laser energy density is calculated, which is found to increase first with laser energy density, and then to decline after reaching a maximum value. Effect of the spatial distribution of laser energy deposition on breakdown depth is analyzed. Meanwhile, the maximum value of breakdown depth is found to decrease as the laser pulse duration becomes shorter.
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Keywords:
- ultrashort-pulse laser /
- dielectric /
- breakdown depth /
- microscopic theoretical model
[1] Bloembergen N 1974 IEEE J. Quantum Electron. 10 375
[2] Holway L H, Fradin D W 1975 J. Appl. Phys. 46 279
[3] Sparks M, Mills D L, Warren R, Holstein T, Maradudin A A, Sham L J, Loh E Jr., King D F 1981 Phys. Rev. B 24 3519
[4] Chen X Q, Zu X T, Zheng W G, Jiang X D, Lü H B, Ren H, Zhang Y Z, Liu C M 2006 Acta Phys. Sin. 55 1201(in Chinese)[陈习权、 祖小涛、 郑万国、 蒋晓东、 吕海兵、 任 寰、 张艳珍、 刘春明 2006 55 1201]
[5] Liang L P, Zhang L, Sheng Y G, Xu Y, Wu D, Sun Y H, Jiang X D, Wei X F 2007 Acta Phys. Sin. 56 3596(in Chinese)[梁丽萍、 张 磊、 盛永刚、 徐 耀、 吴 东、 孙予罕、 蒋晓东、魏晓峰 2007 56 3596]
[6] Han J H, Feng G Y, Yang L M, Zhang Q H, Xie X D, Zhu Q H, Zhou S H 2008 Acta Phys. Sin. 57 5558(in Chinese)[韩敬华、 冯国英、 杨李茗、 张秋慧、 谢旭东、 朱启华、 周寿桓 2008 57 5558]
[7] Dai C J, Chen Z D 2001 Chin. Phys. B 10 403
[8] Chen L M, Zhang J, Lin H, Li Y T, Zhao L Z, Jiang W M 2001 Chin. Phys. B 10 40
[9] Liu H J, Huang J, Wang F R, Zhou X D, Jiang X D, Wu W D 2010 Acta Phys. Sin. 59 1308(in Chinese)[刘红婕、 黄 进、 王凤蕊、 周信达、 蒋旭东、 吴卫东 2010 59 1308]
[10] Zhao X H, Hu J P, Gao Y, Pan F, Ma P 2010 Acta Phys. Sin. 59 3917(in Chinese)[赵兴海、 胡建平、 高 杨、 潘 峰、 马 平 2010 59 3917] 〖11] Du D, Liu X, Korn G, Squier J, Mourou G 1993 Appl. Phys. Lett. 64 3071
[11] Stuart B C, Feit M D, Rubenchik A M, Shore B W, Perry M D 1995 Phys. Rev. Lett. 74 2248
[12] Tien A C, Backus S, Kapteyn H, Murnane M, Mourou G 1999 Phys. Rev. Lett. 82 3883
[13] Jia T Q, Chen H, Wu X 2000 Acta Phys. Sin. 49 1277(in Chinese)[贾天卿、 陈 鸿、 吴 翔 2000 49 1277]
[14] Li C B, Jia T Q, Sun H Y, Li X X, Xu S Z, Feng H D, Wang X F, Ge X C, Xu Z Z 2006 Acta Phys. Sin. 55 0217(in Chinese)[李成斌、 贾天卿、 孙海轶、 李晓溪、 徐世珍、 冯海东、 王晓峰、 葛晓春、 徐至展 2006 55 0217]
[15] Jiang L, Tsai H L 2008 J. Appl. Phys. 104 093101
[16] Sudrie L, Couairon A, Franco M, Lamouroux B, Prade B, Tzotzakis S, Mysyrowicz A 2002 Phys. Rev. Lett. 89 186601
[17] Wu A Q, Chowdhury I H, Xu X 2005 Phys. Rev. B 72 085128
[18] Deng Y P, Jia T Q, Leng Y X, Lu H H, Li R X, Xu Z Z 2004 Acta Phys. Sin. 53 2216(in Chinese)[邓蕴沛、 贾天卿、 冷雨欣、 陆海鹤、 李儒新、 徐至展 2004 53 2216]
[19] Jiang L, Tsai H L 2006 J. Appl. Phys. 100 023116
[20] Frohlich H, Mott N F 1954 Adv. Phys. 3 325
[21] Seitz F 1949 Phys. Rev. 76 1376
[22] Keldysh L V 1965 Sov. Phys. JETP 20 1307
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[1] Bloembergen N 1974 IEEE J. Quantum Electron. 10 375
[2] Holway L H, Fradin D W 1975 J. Appl. Phys. 46 279
[3] Sparks M, Mills D L, Warren R, Holstein T, Maradudin A A, Sham L J, Loh E Jr., King D F 1981 Phys. Rev. B 24 3519
[4] Chen X Q, Zu X T, Zheng W G, Jiang X D, Lü H B, Ren H, Zhang Y Z, Liu C M 2006 Acta Phys. Sin. 55 1201(in Chinese)[陈习权、 祖小涛、 郑万国、 蒋晓东、 吕海兵、 任 寰、 张艳珍、 刘春明 2006 55 1201]
[5] Liang L P, Zhang L, Sheng Y G, Xu Y, Wu D, Sun Y H, Jiang X D, Wei X F 2007 Acta Phys. Sin. 56 3596(in Chinese)[梁丽萍、 张 磊、 盛永刚、 徐 耀、 吴 东、 孙予罕、 蒋晓东、魏晓峰 2007 56 3596]
[6] Han J H, Feng G Y, Yang L M, Zhang Q H, Xie X D, Zhu Q H, Zhou S H 2008 Acta Phys. Sin. 57 5558(in Chinese)[韩敬华、 冯国英、 杨李茗、 张秋慧、 谢旭东、 朱启华、 周寿桓 2008 57 5558]
[7] Dai C J, Chen Z D 2001 Chin. Phys. B 10 403
[8] Chen L M, Zhang J, Lin H, Li Y T, Zhao L Z, Jiang W M 2001 Chin. Phys. B 10 40
[9] Liu H J, Huang J, Wang F R, Zhou X D, Jiang X D, Wu W D 2010 Acta Phys. Sin. 59 1308(in Chinese)[刘红婕、 黄 进、 王凤蕊、 周信达、 蒋旭东、 吴卫东 2010 59 1308]
[10] Zhao X H, Hu J P, Gao Y, Pan F, Ma P 2010 Acta Phys. Sin. 59 3917(in Chinese)[赵兴海、 胡建平、 高 杨、 潘 峰、 马 平 2010 59 3917] 〖11] Du D, Liu X, Korn G, Squier J, Mourou G 1993 Appl. Phys. Lett. 64 3071
[11] Stuart B C, Feit M D, Rubenchik A M, Shore B W, Perry M D 1995 Phys. Rev. Lett. 74 2248
[12] Tien A C, Backus S, Kapteyn H, Murnane M, Mourou G 1999 Phys. Rev. Lett. 82 3883
[13] Jia T Q, Chen H, Wu X 2000 Acta Phys. Sin. 49 1277(in Chinese)[贾天卿、 陈 鸿、 吴 翔 2000 49 1277]
[14] Li C B, Jia T Q, Sun H Y, Li X X, Xu S Z, Feng H D, Wang X F, Ge X C, Xu Z Z 2006 Acta Phys. Sin. 55 0217(in Chinese)[李成斌、 贾天卿、 孙海轶、 李晓溪、 徐世珍、 冯海东、 王晓峰、 葛晓春、 徐至展 2006 55 0217]
[15] Jiang L, Tsai H L 2008 J. Appl. Phys. 104 093101
[16] Sudrie L, Couairon A, Franco M, Lamouroux B, Prade B, Tzotzakis S, Mysyrowicz A 2002 Phys. Rev. Lett. 89 186601
[17] Wu A Q, Chowdhury I H, Xu X 2005 Phys. Rev. B 72 085128
[18] Deng Y P, Jia T Q, Leng Y X, Lu H H, Li R X, Xu Z Z 2004 Acta Phys. Sin. 53 2216(in Chinese)[邓蕴沛、 贾天卿、 冷雨欣、 陆海鹤、 李儒新、 徐至展 2004 53 2216]
[19] Jiang L, Tsai H L 2006 J. Appl. Phys. 100 023116
[20] Frohlich H, Mott N F 1954 Adv. Phys. 3 325
[21] Seitz F 1949 Phys. Rev. 76 1376
[22] Keldysh L V 1965 Sov. Phys. JETP 20 1307
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